Lesson Corporate Finance: Concept of Net Present Value and its usage

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About Shruti_Mishra: I am a maths graduate from India and am currently persuing masters in Operations Research.

The <A HREF=Net_Present_Value.wikipedia>Net Present Value</A> (NPV) of a project is defined as the sum of <A HREF="lesson_PV.lesson">present values</A> (PVs) of annual <A HREF=Cash_Flow.wikipedia>cash flows</A> expected from the project minus the initial investment. Thus it gives the net value of a project or investment. The annual cash flows are the cash inflows - cash outflows for that year. The cash flows are discounted at <A HREF=Discount_Rate.wikipedia>discount rates</A> appropriate to the risk profile of the project. The appropriate discount rate can be calculated as mentioned in <A HREF="PV_rate2use.lesson">Calculating PV - Which interest rate to use </A>

Thus the formula for calculating the NPV can be written as 
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{{{NPV = sum( C[i]/(1+r)^i, i=1, T ) + C[0]}}}
</center>
where {{{C[0]}}} is the initial investment. Since this is mostly a cash outflow, it is usually negative. This includes all the startup costs and investments required for the project. The other variables in the formula are:

{{{C[i]}}}: Cash inflow - Cash outflow for year 'i'.

r: <A HREF=Discount_Rate.wikipedia>Discount Rate</A> -  This is the appropriate discount rate for the risk profile of the project. This is often calculated by considering the return on an alternative investment that can be made if the current project is not taken. This is also known as the opportunity cost.

T: This is the time period of the project/investment.

A company should invest in a project only if it offers positive NPV. A project with negative NPV should be certainly dropped since it means that the present value of the the future cash flows are less than the initial investment made. Theoretically all projects with a positive NPV should be taken up since they offer a positive value. However, due to capital constraints, it is not possible to take all of them. Thus the company selects the projects with highest NPV for the given cash investment. This is done by using NPV index which is calculated by dividing NPV with the initial cash investment. The higher the NPV index, the more profitable the investment is (higher return) and more likely its selection.